| Piezoelectric ceramic actuators (PCAs) based on inverse piezoelectric effect havebeen widely used in precision positioning systems due to their apparent advantages,such as the small size, high energy density, high resolution, and quick frequencyresponse. The output displacement of single-wafer PCAs is relatively small, so thatpiezoelectric ceramic stack actuators (PCSAs), which are realized by assemblingmulti-chip piezoelectric ceramic wafers and electrodes, are the best choice to achievelarge output displacement with high resolution. However, some of the shortcomings ofPCSAs fabricated by layering/stacking processes greatly limit their applications in fastand high-precision positioning systems. Firstly, the hysteretic behavior of PCSAs isfurther worsened because of the accumulation of the hysteretic behavior of piezoelectricceramic wafers, so how to effectively control PCSAs is difficult and emphasized inprecise positioning systems; secondly, the different layering/stacking processes greatlyaffect the dynamic performances of PCSAs, even possibly shorten the life of PCSAs. Inthese cases, in order to let PCSAs be used in fast and high-precision positioning systems,it is urgent to study the linearization control method, which can linearize the hysteresisbehavior of PCSAs and PCSAs’ based systems, and the method to design dynamicperformance of PCSAs. Carrying out these methods has an important academicsignificance and prospect of engineering application.In this dissertation, in order to solve the above problems, a Bouc-Wenmathematical model for PCSAs to characterize the hysteresis behavior of PCSAs is putforward. Based on the proposed Bouc-Wen mathematical model for PCSAs, twolinearization control methods to linearize the hysteresis behavior of PCSAs areproposed and realized. In order to design dynamic performance of PCSAs, acomprehensive model that can accurately simulate the hysteresis behavior and thedynamic performance of PCSAs is put forward and a method to design dynamicperformance of PCSAs is established based on the proposed comprehensive model forPCSAs. In these cases, a phenomenon model for pre-stressed PCSAs is established andinvestigated and a robust model reference adaptive control method for atwo-dimensional piezo-driven micro-displacement scanning platform (2D-PDMDSP)based on the proposed phenomenon model is put forward.The major research works and the innovations in this dissertation are summarized as follows1. A Bouc-Wen mathematical model for PCSAs which can model the hysteresisbehavior of PCSAs is proposed, and a corresponding parameter identification method,which can identify the parameters by obtaining analytical solutions, is established. Inthe parameter identification, the least-squares method is used to reduce external randomdisturbances. The performance of the Bouc-Wen mathematical model with thecorresponding parameter identification method is experimentally verified by theestablished experimental setup. The experimental results show that the Bouc-Wenmathematical model can simulate PCSAs and the modeling errors are about3%.2. A non-symmetrical Bouc-Wen hysteresis operator for modeling thenon-symmetrical hysteresis of PCSAs is established by introducing a non-symmetricalformula into the Bouc-Wen hysteresis operator. Accordingly, a non-symmetricalBouc-Wen mathematical model for PCSAs is put forward by modeling thenon-symmetrical hysteresis component of PCSAs with the non-symmetrical Bouc-Wenhysteresis operator, and a corresponding parameter identification method, which canidentify the parameters by obtaining analytical solutions, is established. Theperformance of the non-symmetrical Bouc-Wen mathematical model with thecorresponding parameter identification method is experimentally verified by theestablished experimental setup. The experimental results show that the non-symmetricalBouc-Wen mathematical model can simulate PCSAs with the non-symmetricalhysteresis more accurately than the Bouc-Wen mathematical model, and the modelingerrors are decreased by about30%. The proposed non-symmetrical Bouc-Wenmathematical model with the corresponding parameter identification method can also beused to model other materials and systems with the non-symmetrical hysteresis.3. In order to linearize the hysteresis behavior of PCSAs, the feedforwardlinearization method based on the proposed Bouc-Wen mathematical model and thehybrid linearization method combining the feedforward and PI feedback loop tolinearize the hysteresis behavior of PCSAs are proposed and explored. The rapid controlprototypes of the linearization controllers for PCSAs using the proposed feedforwardand hybrid linearization methods with rapid control prototyping technique based on thereal-time simulation system are established and experimentally tested. The experimentalresults show that both the feedforward and hybrid linearization methods for PCSAs canlinearize the hysteresis behavior of PCSAs, and the proposed hybrid linearizationmethod can reach higher linearization accuracy than the feedforward linearization method. Utilizing the proposed linearization methods, the open-loop and closed-loopcontrols for the tip displacement of a piezoelectric-driven microgripper are realized,which indicates that the proposed linearization methods can simplify the control for thepiezoelectric-driven microgripper with high accuracy.4. Considering the bonding layers as passive single-DOF mass-damping-stiffnesssystems, a comprehensive model for PCSAs based on the Bouc-Wen hysteresis operator,which can simulate both the hysteresis behavior and the dynamic performance ofPCSAs, is proposed. According to the proposed comprehensive model, thelayering/stacking processes of PCSAs change the dynamic performance of PCSAs bychanging the parameters of the bonding layers but can’t affect the hysteresis behavior ofPCSAs, which is consistent with the experimental results. Letting PCSAs bepre-stressed with elastic deformation mechanisms, a method to determine themechanical parameters of pre-stressed mechanisms of PCSAs is proposed. Thesimulation results show that the proposed method can effectively design the dynamicperformance of PCSAs to some extent.5. A phenomenological model for modeling the hysteresis behavior and thedynamic performance of pre-stressed PCSAs by using the Bouc-Wen hysteresis operator,as well as the corresponding parameter identification method, is proposed. Theperformance of the phenomenological model with the corresponding parameteridentification method is experimentally verified by the established experimental setup.The experimental results show that the proposed phenomenological model forpre-stressed PCSAs with the corresponding parameter identification method canaccurately model the hysteresis behavior and the dynamic performance of pre-stressedPCSAs.6. Based on the afore-mentioned works, a phenomenological model for the2D-PDMDSP is established. Accordingly, a robust model reference adaptive controlmethod for the2D-PDMDSP is proposed and established and the stability istheoretically proved. The proposed control method is experimentally verified by theestablished experimental setup and the corresponding controlled results are comparedwith those by the PID control method based on the proposed phenomenon model. Theexperimental results show that robust model reference adaptive control method cansignificantly improve the accuracy of the positioning with high robustness and learningability.The research results on the hysteretic modeling, linearization, and control method for PCSAs and PCSAs’ based systems has established the theoretical foundation forapplying PCSAs in fast and high-precision positioning systems. |
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